Outlier robust corner-preserving methods for reconstructing noisy images

Details Outlier robust corner-preserving methods for reconstructing noisy images Outlier robust corner-preserving methods for reconstructing noisy images

2007-08-03

arxiv.org/abs/0708.0481v1

Annals of Statistics 2007, Vol. 35, No. 1, 132-165

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053606000001109 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053606000001109

The ability to remove a large amount of noise and the ability to preserve most structure are desirable properties of an image smoother. Unfortunately, they usually seem to be at odds with each other; one can only improve one property at the cost of the other. By combining M-smoothing and least-squares-trimming, the TM-smoother is introduced as a means to unify corner-preserving properties and outlier robustness. To identify edge- and corner-preserving properties, a new theory based on differential geometry is developed. Further, robustness concepts are transferred to image processing. In two examples, the TM-smoother outperforms other corner-preserving smoothers. A software package containing both the TM- and the M-smoother can be downloaded from the Internet.

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